C₄×D₃×Q₁₆ #79716

order	384
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

C₄×D₃×Q₁₆

Fitting	C₃×C₄×Q₁₆ ⋊ C₂
Sylow	C₃ ⋊ C₂×C₄×Q₁₆

488 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 4 generators on 23 points:

(5,7,9,15)(6,10,12,19)(8,17,18,14)(11,20,16,13)(21,22,23);(5,6,9,12)(7,13,15,20)(8,16,18,11)(10,17,19,14);(22,23);(1,2,3,4)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 12292);